where the fermionic and bosonic densities (\(n_F({\bf r},t)\) , \(n_B({\bf r},t)\) ) and irrotational velocity fields (\({\bf {v}}_{\!F}({\bf r},t)\) , \({\bf {v}}_{\!B}({\bf r},t)\) ) are used as main variables. Different terms in the right-hand side of Eqs. (REF ) (the second and the fourth ones) represent various energy components present in the system under consideration. \(T\)  is the intrinsic kinetic energy of an ideal Fermi gas and is calculated including lowest order gradient correction [1]}, [2]}, [3]} and \(E_{BF}\)  is the boson-fermion interaction energy. \(E_{BF}\)  includes the mean-field term and a quantum corrections due to quantum fluctuations which is necessary to stabilize the Bose-Fermi droplet [4]}. The term \(E_B\)  describes the interaction between bosons, including the famous Lee-Huang-Yang correction [5]}, \(V_q\)  is related to the bosonic quantum pressure [6]}. Terms proportional to the square of velocities represent the energies of macroscopic flow of bosonic and fermionic fluids. Detailed formulas are given in Appendix .
